He used old drawings of Mars dating back to 1666 to try to determine the sidereal day of Mars. His final estimate, in 1873, was 24h 37m 22.713s, reasonably close to the modern value of 24h 37m 22.663s.[1][2][3] Nevertheless, Frederik Kaiser's value of 24h 37m 22.622s is closer.

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He was a delicate child, and, his father dying in 1850, his mother attended herself to his education. On his health improving he was sent to King's College London, and subsequently earned a scholarship at St John's College, Cambridge. He graduated in 1860 as 23rd wrangler.[4] His marriage while still an undergraduate probably accounted for his low place in the tripos.

He then read for the bar, but turned to astronomy and authorship instead, and in 1865 published an article on the Colors of Double Stars in the Cornhill Magazine. His first book Saturn and its System was published in the same year, at his own expense. This work contains an elaborate account of the phenomena presented by the planet; but although favourably received by astronomers, it had no great sale. He intended to follow it up with similar treatises on Mars, Jupiter, Sun, Moon, comets and meteors, stars, and nebulae, and had in fact commenced a monograph on Mars, when the failure of a New Zealand bank deprived him of an independence which would have enabled him to carry out his scheme without anxiety as to its commercial success or failure.

Being thus obliged to depend upon his writings for the support of his family, and having learned by the fate of his Saturn and its System that the general public are not attracted by works requiring arduous study, he cultivated a more popular style. He wrote for a number of periodicals; and although he has stated that he would at this time willingly have turned to stone-breaking on the roads, or any other form of hard and honest but unscientific labour, if a modest competence had been offered him in any such direction, he attained a high degree of popularity, and his numerous works had a wide influence in familiarising the public with the main facts of astronomy.

His earlier efforts were, however, not always successful. His Handbook of the Stars (1866) was refused by Messrs Longmans and Messrs Macmillan, but being privately printed, it sold fairly well. For his Half-Hours with the Telescope (1868), which eventually reached a 20th edition, he received originally £25 from Messrs Hardwick. Although teaching was uncongenial to him he took pupils in mathematics, and held for a time the position of mathematical coach for Woolwich and Sandhurst.

His literary standing meantime improved, and he became a regular contributor to The Intellectual Observer, Chamber's Journal and the Popular Science Review. In 1870 appeared his Other Worlds Than Ours,[5] in which he discussed the question of the plurality of worlds in the light of new facts. This was followed by a long series of popular treatises in rapid succession, amongst the more important of which are Light Science for Leisure Hours and The Sun (1871); The Orbs around Us and Essays on Astronomy (1872); The Expanse of Heaven, The Moon and The Borderland of Science (1873); The Universe and the Coming Transits and Transits of Venus (1874); Our Place among Infinities (1875); Myths and Marvels of Astronomy (1877); The Universe of Stars (1878); Flowers of the Sky (1879); The Poetry of Astronomy (1880); Easy Star Lessons and Familiar Science Studies (1882); Mysteries of Time and Space and The Great Pyramid (1883); The Universe of Suns (1884); The Seasons (1885); Other Suns than Ours and Half-Hours with the Stars (1887).

In 1881 he founded Knowledge, a popular weekly magazine of science (converted into a monthly in 1885), which had a considerable circulation. In it he wrote on a great variety of subjects, including chess and whist.

Elected a fellow of the Royal Astronomical Society in 1866, he became honorary secretary in 1872, and contributed eighty-three separate papers to its Monthly Notices. Of these the more noteworthy dealt with the distribution of stars, star clusters and nebulae, and the construction of the sidereal universe. He was an expert in all that related to map-drawing, and published two star-atlases. A chart on an isographic projection, exhibiting all the stars contained in the Bonner Durchmusterung, was designed to show the laws according to which the stars down to the 9–10th magnitude are distributed over the northern heavens. His Theoretical Considerations respecting the Corona (Monthly Notices, xxxi. 184, 254) also deserve mention, as well as his discussions of the rotation of Mars, by which be deduced its period with a probable error of 0.005. He also vigorously criticised the official arrangements for observing the transits of Venus of 1874 and 1882.

His largest and most ambitious work, Old and New Astronomy, left unfinished at his death, was completed by Arthur Cowper Ranyard and published in 1892. He settled in America some time after his second marriage in 1881, and died of yellow fever at New York City on 12 September 1888. A monument was later erected in his memory.[6]Mary Proctor, his daughter by his first marriage, became an astronomer and a successful lecturer and writer.